{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:7NYIO7UPN4JO7LPXWEQDQDH4IN","short_pith_number":"pith:7NYIO7UP","canonical_record":{"source":{"id":"1311.6830","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.FL","submitted_at":"2013-11-26T21:58:47Z","cross_cats_sorted":["cs.DM"],"title_canon_sha256":"45132c7c781f25c9b9955e0c2d9187bf534831e0c21087c05e31d5cf8af59a06","abstract_canon_sha256":"2de143f15b8b7207975ca68658d4981c5702734882720f35ebc94b680ef2e32d"},"schema_version":"1.0"},"canonical_sha256":"fb70877e8f6f12efadf7b120380cfc436dbf44c7721dd2e905184d425b8512df","source":{"kind":"arxiv","id":"1311.6830","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1311.6830","created_at":"2026-05-18T03:06:05Z"},{"alias_kind":"arxiv_version","alias_value":"1311.6830v1","created_at":"2026-05-18T03:06:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1311.6830","created_at":"2026-05-18T03:06:05Z"},{"alias_kind":"pith_short_12","alias_value":"7NYIO7UPN4JO","created_at":"2026-05-18T12:27:36Z"},{"alias_kind":"pith_short_16","alias_value":"7NYIO7UPN4JO7LPX","created_at":"2026-05-18T12:27:36Z"},{"alias_kind":"pith_short_8","alias_value":"7NYIO7UP","created_at":"2026-05-18T12:27:36Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:7NYIO7UPN4JO7LPXWEQDQDH4IN","target":"record","payload":{"canonical_record":{"source":{"id":"1311.6830","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.FL","submitted_at":"2013-11-26T21:58:47Z","cross_cats_sorted":["cs.DM"],"title_canon_sha256":"45132c7c781f25c9b9955e0c2d9187bf534831e0c21087c05e31d5cf8af59a06","abstract_canon_sha256":"2de143f15b8b7207975ca68658d4981c5702734882720f35ebc94b680ef2e32d"},"schema_version":"1.0"},"canonical_sha256":"fb70877e8f6f12efadf7b120380cfc436dbf44c7721dd2e905184d425b8512df","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:06:05.374424Z","signature_b64":"P5aCRi1ThkEtVo9XrXIFqvllC9YWavO4/ObUdatbZQlyNfEtVsoAOQRIi35Y6kt+6/neeMyOx6kT7QOtwl2qBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fb70877e8f6f12efadf7b120380cfc436dbf44c7721dd2e905184d425b8512df","last_reissued_at":"2026-05-18T03:06:05.373988Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:06:05.373988Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1311.6830","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:06:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HlZef0Hn3w1lhkoSx5XSTiBbaKp+1uOPnNciCZaa55iA45OfOH9C21qEeYrItyqbKax+butSPH4kctVoNLWmBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T18:18:31.130628Z"},"content_sha256":"d43c4063324dc26dcc6e57fc7e8c1f4f93327d68d64915dae2f07f69b0d0ccaf","schema_version":"1.0","event_id":"sha256:d43c4063324dc26dcc6e57fc7e8c1f4f93327d68d64915dae2f07f69b0d0ccaf"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:7NYIO7UPN4JO7LPXWEQDQDH4IN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Ergodicity of Random Walks on Random DFA","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"cs.FL","authors_text":"Borja Balle","submitted_at":"2013-11-26T21:58:47Z","abstract_excerpt":"Given a DFA we consider the random walk that starts at the initial state and at each time step moves to a new state by taking a random transition from the current state. This paper shows that for typical DFA this random walk induces an ergodic Markov chain. The notion of typical DFA is formalized by showing that ergodicity holds with high probability when a DFA is sampled uniformly at random from the set of all automata with a fixed number of states. We also show the same result applies to DFA obtained by minimizing typical DFA."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.6830","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:06:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gzaqs8V4w4tW4cxEZZeHRFjEtuGMHxf9g4ni1iI26SzBIuCpjmbHEdje1Jx8DIHgkf1cc3q11omCG4VAbAKSAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T18:18:31.130978Z"},"content_sha256":"9d49e9b63f727fcc31def1d85cf4e1157f8b7b0a35a6b1673572e7877ef05c73","schema_version":"1.0","event_id":"sha256:9d49e9b63f727fcc31def1d85cf4e1157f8b7b0a35a6b1673572e7877ef05c73"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7NYIO7UPN4JO7LPXWEQDQDH4IN/bundle.json","state_url":"https://pith.science/pith/7NYIO7UPN4JO7LPXWEQDQDH4IN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7NYIO7UPN4JO7LPXWEQDQDH4IN/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-01T18:18:31Z","links":{"resolver":"https://pith.science/pith/7NYIO7UPN4JO7LPXWEQDQDH4IN","bundle":"https://pith.science/pith/7NYIO7UPN4JO7LPXWEQDQDH4IN/bundle.json","state":"https://pith.science/pith/7NYIO7UPN4JO7LPXWEQDQDH4IN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7NYIO7UPN4JO7LPXWEQDQDH4IN/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:7NYIO7UPN4JO7LPXWEQDQDH4IN","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"2de143f15b8b7207975ca68658d4981c5702734882720f35ebc94b680ef2e32d","cross_cats_sorted":["cs.DM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.FL","submitted_at":"2013-11-26T21:58:47Z","title_canon_sha256":"45132c7c781f25c9b9955e0c2d9187bf534831e0c21087c05e31d5cf8af59a06"},"schema_version":"1.0","source":{"id":"1311.6830","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1311.6830","created_at":"2026-05-18T03:06:05Z"},{"alias_kind":"arxiv_version","alias_value":"1311.6830v1","created_at":"2026-05-18T03:06:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1311.6830","created_at":"2026-05-18T03:06:05Z"},{"alias_kind":"pith_short_12","alias_value":"7NYIO7UPN4JO","created_at":"2026-05-18T12:27:36Z"},{"alias_kind":"pith_short_16","alias_value":"7NYIO7UPN4JO7LPX","created_at":"2026-05-18T12:27:36Z"},{"alias_kind":"pith_short_8","alias_value":"7NYIO7UP","created_at":"2026-05-18T12:27:36Z"}],"graph_snapshots":[{"event_id":"sha256:9d49e9b63f727fcc31def1d85cf4e1157f8b7b0a35a6b1673572e7877ef05c73","target":"graph","created_at":"2026-05-18T03:06:05Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"Given a DFA we consider the random walk that starts at the initial state and at each time step moves to a new state by taking a random transition from the current state. This paper shows that for typical DFA this random walk induces an ergodic Markov chain. The notion of typical DFA is formalized by showing that ergodicity holds with high probability when a DFA is sampled uniformly at random from the set of all automata with a fixed number of states. We also show the same result applies to DFA obtained by minimizing typical DFA.","authors_text":"Borja Balle","cross_cats":["cs.DM"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.FL","submitted_at":"2013-11-26T21:58:47Z","title":"Ergodicity of Random Walks on Random DFA"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.6830","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:d43c4063324dc26dcc6e57fc7e8c1f4f93327d68d64915dae2f07f69b0d0ccaf","target":"record","created_at":"2026-05-18T03:06:05Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"2de143f15b8b7207975ca68658d4981c5702734882720f35ebc94b680ef2e32d","cross_cats_sorted":["cs.DM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.FL","submitted_at":"2013-11-26T21:58:47Z","title_canon_sha256":"45132c7c781f25c9b9955e0c2d9187bf534831e0c21087c05e31d5cf8af59a06"},"schema_version":"1.0","source":{"id":"1311.6830","kind":"arxiv","version":1}},"canonical_sha256":"fb70877e8f6f12efadf7b120380cfc436dbf44c7721dd2e905184d425b8512df","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fb70877e8f6f12efadf7b120380cfc436dbf44c7721dd2e905184d425b8512df","first_computed_at":"2026-05-18T03:06:05.373988Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:06:05.373988Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"P5aCRi1ThkEtVo9XrXIFqvllC9YWavO4/ObUdatbZQlyNfEtVsoAOQRIi35Y6kt+6/neeMyOx6kT7QOtwl2qBg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:06:05.374424Z","signed_message":"canonical_sha256_bytes"},"source_id":"1311.6830","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d43c4063324dc26dcc6e57fc7e8c1f4f93327d68d64915dae2f07f69b0d0ccaf","sha256:9d49e9b63f727fcc31def1d85cf4e1157f8b7b0a35a6b1673572e7877ef05c73"],"state_sha256":"9743f87bf7d4423b766eb0bfe3996a6aac7339d0f9a6a4431f8247312492ba15"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0i0hTMwZhMBXrno5jq77se+LI8TTD1TOnr1Z6UT3NAYuaHsc1s7wR5CnAQetlG+Io4GIIxw/JgM79Om/VY2RCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T18:18:31.133138Z","bundle_sha256":"be861009014f907dc229d85f0f532ef58c40f5cb50cb03e3fa78ee8c9ca91328"}}